2019
DOI: 10.1051/proc/201965068
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New particle representations for ergodic McKean-Vlasov SDEs

Abstract: The aim of this paper is to introduce several new particle representations for ergodic McKean-Vlasov SDEs. We construct new algorithms by leveraging recent progress in weak convergence analysis of interacting particle system. We present detailed analysis of errors and associated costs of various estimators, highlighting key differences between long-time simulations of linear (classical SDEs) versus non-linear (Mckean-Vlasov SDEs) process. 2010

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Cited by 7 publications
(8 citation statements)
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“…where W i , 1 ≤ i ≤ N , are k-dimensional, mutually independent Brownian motions, Law(X i 0 ) = µ X 0 and µ X,N t is defined in (2). We will briefly illustrate that this particle system is well-posed.…”
Section: Time-stepping Scheme and Main Resultsmentioning
confidence: 99%
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“…where W i , 1 ≤ i ≤ N , are k-dimensional, mutually independent Brownian motions, Law(X i 0 ) = µ X 0 and µ X,N t is defined in (2). We will briefly illustrate that this particle system is well-posed.…”
Section: Time-stepping Scheme and Main Resultsmentioning
confidence: 99%
“…∇ 2 σ i (x)(h (1) , h (2) ) and ∇ 2 σ i (x) : R d × R d → R d has to be understood as an operator defined as ∇ 2 σ i (x)(h (1) , h (2) ) := d l,j=1…”
Section: A Tamed Milstein Schemementioning
confidence: 99%
“…We also mention that applications of Probability Theory to compartmental models involve furthermore Large Deviation Principles for stochastic models, [27,19,28]. Finally, besides topic related literature, we would like to mention some works whose techniques inspired the present one, [10,11,14,1,12,13].…”
Section: Besides a Factormentioning
confidence: 93%
“…The former case is very difficult and we have not identified yet the solution. Indeed, in Theorem 1.2 we only consider the second case, in the restricted regime β < 1 3 , which we might dub "intermediate interactions", closely related to the result on moderate interactions of [24,25,26,22,16,31,15].…”
Section: Besides a Factormentioning
confidence: 99%
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